Coherent detection is a well-established technique in telecommunication and spectroscopy. It refers to the detection of the interference between a reference signal (often referred to as a ‘local oscillator’) having a large power (compared to the noise level of the detector) and a weak measurement signal, as a way to extract the information (power) of the weak signal. The interference signal is modulated at the difference frequency between the local oscillator and the weak signal.
Coherent amplification results when a signal interferes with a local oscillator to produce a heterodyne coherent beat on a detector:P(t)Coherent,i=P(t)ref,i+P(t)s,i+2√{square root over (P(t)ref,i·P(t)s,i)}·cos [(ωref,i−ωs,i)t]where P(t)Coherent,i is the coherent power interference on detector, P(t)ref,i is the reference pulse power, P(t)s,i is the signal pulse power, ωref,i is the reference frequency, and ωs,i is the signal frequency. Typically, the frequency of reference and signal are fixed resulting in a constant difference frequency beat in the detector. For homodyne detection, the difference frequency Δω=(ωref−ωs) is nominally zero and the information is coded either in the phase difference between signal and reference or in a frequency shift of the signal. For heterodyne detection, the difference frequency is not nominally zero. The beat frequency is the modulation frequency Δω of the heterodyne signal. When the beat frequency is constant, its intensity can be extracted by using a band-pass filter centered at Δω, lock-in amplification, or using other signal recovery methods.
Both reference and signal can be derived from a single laser source. A heterodyne signal can be generated if a phase-modulation or frequency shift is provided to either reference or signal. For example, a frequency-shifted reference signal can be obtained from a single laser source using an acousto-optic modulator (AOM). Alternatively, phase-modulation can be realized by electro-optic modulators (EOM) or piezo-electric phase modulators. Coherent detection by phase-modulation is known as pseudo-heterodyne detection.
In optical double-comb spectroscopy, the difference frequency is not zero and each wavelength channel used for spectroscopy has a unique (multiple of a known base) difference frequency. The amplitude of each beat difference frequency is measured (in the RF domain) and is assigned to the spectrum sample centered at the corresponding frequency of the signal laser. Implementation of sources for a double-comb spectroscopy is however difficult.